A Theory of Interactive Parallel Processing: New Capacity Measures and Predictions for a Response Time Inequality Series

Townsend, J. T., & Wenger, M. J. (2004). A Theory of Interactive Parallel Processing: New Capacity Measures and Predictions for a Response Time Inequality Series. Psychological Review, 111(4), 1003-1035.

Abstract:
The authors present a theory of stochastic interactive parallel processing with special emphasis on channel interactions and their relation to system capacity. The approach is based both on linear systems theory augmented with stochastic elements and decisional operators and on a metatheory of parallel channels' dependencies that incorporates standard independent and coactive parallel models as special cases. The metatheory is applied to OR and AND experimental paradigms, and the authors establish new theorems relating response time performance in these designs to earlier and novel issues. One notable outcome is the remarkable processing efficiency associated with linear parallel-channel systems that include mutually positive interactions. The results may offer insight into perceptual and cognitive configural-holistic processing systems.

Note:
This paper addressed that capacity may be affected by the dependency between the channels (cross-talk), and the decision operator (OR/ AND).

UCIP processing means that channels are independent (zero correlation). The dependency occurs when the channels interact with each other. A positive correlation may lead to a supercapacity processing; a negative correlation may lead to a limited capacity processing.

Decision operators may be OR or AND. The OR process means that observers respond yes when either target is presented (minimum reaction time, self-terminating, first-terminating). The AND process means that observers respond yes when both targets were presented.

The performance with OR operation should be compared with Miller inequality (supercapactiy), and with Grice inequality (limited capacity). Simulated data showed that channels with positive correlation may violate the Miller inequality, and those with negative correlation may violate the Grice inequality.

The performance with AND operation should be compared with Colonius-Vorberg (CV bound). Simulated data showed that channels with positive correlation may violate the upper CV bound, and those with negative correlation may violate the lower CV bound.

The coactivation model is not affected by the correlation between channels. Data in coactivation with positive, negative or zero correlation between channels violates the Miller inequality, but does not violate the Grice inequality.

When we measure the capacity limitation, we should consider the dependency between channels and the decision operator.